Final answer:
The student is attempting to find the measure of an angle ø whose terminal side is in the fourth quadrant, with a given cotangent value. The angle can be found using the arctangent function, and the sign of the tangent confirms the angle is indeed in the fourth quadrant.
Step-by-step explanation:
The question deals with finding the angle ø in standard position where the terminal side is in the fourth quadrant, and given that cot ø = -7/18. Since cotangent is the reciprocal of tangent, we have cot ø = 1/tan ø, implying that tan ø = -18/7. In the fourth quadrant, tangent is negative because it is the ratio of the sine to cosine, and in the fourth quadrant, sine is negative while cosine is positive.
To find the angle, we would use the arctangent function, noting that tangent is negative, which is standard for angles in the fourth quadrant, where ø = tan¹ (-18/7). The exact degree measure can be found using a calculator. Since angles are defined as positive in the counter-clockwise direction, ø would be the angle measured counter-clockwise from the positive x-axis to the terminal side of the angle in the fourth quadrant.